Bellwork Copy and Answer
5 – 76 + -15-14 - -106 x -7-5 ÷ -5-10 x -10
2
Tuesday 10/18
2-5 Solving Equations
Containing Integerspg. 100
Essential Question
How can you solve equations that contain integers?
5
Who REMEMBERS?
Monday we talked about 3 steps to solve an equation.
What are the 3 steps? I___________ S___________ C___________
5
Steps to Solving Equations:
1. Use the opposite operation to ISOLATE the variable to one side of the equation
2. SOLVE for the Variable3. CHECK the answer to the equation by
substituting the number in for the variable
7
Equation Mat
Today we will use an Equation Mat and Integer Chips to model solving an equation.
LAB
7
Equation Mat Directions… Yellow=positive 1 Red= negative 1 Use the chips for our numbers. If the equation is x+3=5…on your mat you should
have
x + =
Then, use your red chips to solve the equation. The red and yellow chips cancel out. We are left with 2 yellow chips, so x=2.
Equation Mat Equations
x + 3=5 x + 4=9 x + 5=8 x + 6=6 x - 4=3 x - 2=8 x - 5=-5 x - 7=0
X=2
X=5
X=3
X=0
X=7
X=10
X=0
X=7
10
Wednesday 10/19
2-5 Solving Equations Containing Integers
pg. 100
Essential Question
How can you solve equations that contain integers?
13
Algebra Geek Patrol
The Pocket Protectors of Algebra
14
My name is Buck Einstein, but you can call me Buck.
Hello!
Pick my nose to continue
15
It’s that we on the Algebra Geek Patrol are… well…different.
I have a secret to tell you. What is it?
You might even say that we are the opposite of everyone else.
Pick my nose to continue
16
When you worry about what you wear,
We worry about having our Pocket Protectors.
Pick my nose to continue
17
When you worry that you won’t meet your friends,
We worry that we won’t have our calculators.
Pick my nose to continue
18
We are just a little bit opposite. That may be why we are so good at Algebra, because that is all Algebra is…
Pick my nose to continue
…doing the opposite.
19
Think of some words that are opposites. For example, what do you think of as the opposite of word below.
Pick my nose to continue
Old = ______ New
20
Now try some other ones. Make sure to write your answers on your paper, and when you are finished click on me.
Pick my nose to continue
Up = __________
Out = __________
Small = __________
Stinky = __________
21
Some possible answers are…
Pick my nose to continue
Up = __________
Out = __________
Small = __________
Stinky = __________
Down
In
Big
Fragrant(or non-stinky)
22
Now another set. Make sure to write your answers on your paper, and when you are finished click on me.
Pick my nose to continue
Add = __________
Subtract = __________
Multiply = __________
Divide = __________
23
Your answers should have been…
Pick my nose to continue
Add = __________
Subtract = __________
Multiply = __________
Divide = __________
Subtract
Add
Divide
Multiply
24
One last set. Make sure to write your answers on your paper, and when you are finished click on me.
Pick my nose to continue
+ = __________
- = __________
x = __________
÷ = __________
25
Your answers should have been…
Pick my nose to continue
+ = __________
- = __________
x = __________
÷ = __________
-
+
÷
x
26
Congratulations!You just did some
ALGEBRA
Pick my nose to continue
Scary, isn’t it!
27
One Step Equations
Algebra Geek Patrol
Now you are going to work on solving some Algebra problems. Don’t be afraid of the A-word (Algebra). Remember, it is all about being opposite.
Pick my nose to continue
28
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
You will complete 5 sections. After each section you will be awarded a Geek Pen to put in your official AGP Pocket Protector.
Geek Luck!
29
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
X + 3 = 17Click on the answer below that is the opposite of add 3.
Add 3Subtract 3Multiply 3
Divide 3
30
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Close, but that’s not quite it.
Remember, we are looking for the opposite of add 3.
Click on Buck and give it another try.
31
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Good Job!
The correct answer is subtract 3.
Write the answer on your paper, next to the original problem, and then click on Buck.
32
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
4x = 20
Click on the answer below that is the opposite of multiply by 4.
Add 4Subtract 4
Multiply by 4
Divide by 4
33
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
No, not really.
Remember, we are looking for the opposite of multiply by 4.
Click on Buck and give it another try.
34
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Nice! You’re halfway to your first Geek Pen.The correct answer is divide by
4.Write the answer on your paper next to the original problem, and then click on Buck.
35
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
x 5
Click on the answer below that is the opposite of divide by 5.
Add 5Subtract 5
Multiply by 5
Divide by 5
= 10
36
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Uhh, in a word, no.
Remember, we are looking for the opposite of divide by 5.
Click on Buck and give it another try.
37
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Good! Are you sure you’re not
a Geek? The correct answer is multiply by 5.
Write the answer on your paper next to the original problem, and then click on Buck.
38
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Click on the answer below that is the opposite of - 7.
+ 7- 7
x 7
÷ 7
X – 7 = 8
39
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Almost
Remember, we are looking for the opposite of - 7.
Click on Buck and give it another try.
40
Algebra Geek Patrol
One Step Equations
Congratulations!
The correct answer is + 7.
Write the answer on your paper next to the original problem, and then click on Buck.
And here is your first Geek Pen
Algebra
Geek
Patrol
41
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
Alright, now you are going to actually solve some problems. This is nothing to be worried about, just remember one word…
Opposite!
Geek Luck!
42
1
One Step Equations
Click on the answer below that is the opposite of + 5.
+ 5- 5
x 5
÷ 5
X + 5 = 13
Algebra
Geek
Patrol
43
1
One Step Equations
C’mon, You know this.Remember, we are looking
for the opposite of + 5.
Click on Buck and give it another try.
Algebra
Geek
Patrol
44
1
One Step Equations
Good!
So, let’s put – 5 on each side of the equation.
Algebra
Geek
Patrol
X + 5 = 13 - 5 - 5_________
Let’s look at the left side. What will you get when you combine + 5 and -5 ?
That’s right, zero. And zero is nothing, so let’s cancel out + 5 and -5.
Click on the pen when you are ready.
Click on +5 or -5 to cancel them.
Now to the hard part.
X =
Just teasing!Look at the right side. All we have left is 13 and – 5. So,what is 13 – 5?
That’s right! 8
That just leaves X on the left side.Copy the entire problem and all the steps on your paper, then click on Buck.
45
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
Congratulations, You just completed your first Algebra problem. See it wasn’t that bad.
Now let’s try another.
46
Who REMEMBERS?
What are the 3 steps to solve a one step equation? I___________ S___________ C___________
46
Steps to Solving Equations:
1. ISOLATE the variable by doing the opposite, Inverse, Operation.
2. SOLVE the equation.3. CHECK your solution.
48
2
One Step Equations
Click on the answer below that is the opposite of + 9.
+ 9- 9
x 9
÷ 9
X + 9 = 15
Algebra
Geek
Patrol
49
2
One Step Equations
Umm, I don’t think so.Remember, we are looking
for the opposite of + 9.
Click on Buck and give it another try.
Algebra
Geek
Patrol
50
2
One Step Equations
Nice Job!
Algebra
Geek
Patrol
X + 9 = 15 - 9 - 9_________
X = 6 Make sure you have copied all the steps on your paper and then click on Buck.
This time I am going to give you the steps, which you will need
to write down, and then you will work the problem on your
paper.
First, put the opposite (- 9) on both sides.
Second, cancel out one side.Write this on your paper, and work this part of the
problem.Click the pen to continue
Third, combine the other side.
Pick my nose to continue
51
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
Congratulations Again, Now let’s try one last problem.
52
Go ahead and give it a try!
3
One Step Equations
X + 7 = 9
Algebra
Geek
Patrol
This time you are going to work the problem on your
paper first and then we will go through it.
Pick my nose when you are finished
Are you sure you are done? Check your answer before moving
on. No one will know but you and me.
53
3
One Step Equations
Algebra
Geek
Patrol
X + 7 = 9 - 7 - 7_________
X = 2 First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.
Make sure you have copied all the steps on your paper and then click on Buck.
Click the pen to continue
54
Algebra Geek Patrol
Algebra
Geek
Patrol
One Step Equations
Nice Work
You are one pen closer to being an Official Algebra
Geek
Don’t worry, I won’t tell
anyone.
Pick my nose to continue
55
Now, try these on your own! X + -6 = 10 -5 + x = -12
56
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
This time let’s try some different types of problems. Since you have gotten so good at this, let’s skip the first part, and go straight to the problems by using the 3 steps.
And remember, today’s word is…
Opposite!
57
1
One Step Equations
Click on the answer below that is the opposite of - 4.
+ 4- 4
x 4
÷ 4
X - 4 = 11
Algebra
Geek
Patrol
58
1
One Step Equations
Nope, try again. Remember, we are looking
for the opposite of - 4.
Click on Buck and give it another try.
Algebra
Geek
Patrol
59
I know all the cool words.
1
One Step Equations
Sweet!
X - 4 = 11_________ +4 +4
X = 15Make sure you have copied all the steps on your paper and then click on Buck.
This time I am going to give you the steps, which you will need to write down, and then you will do
the problem on your paper.
First, put the opposite (+4) on both sides.Second, cancel out one side.
Write this on your paper, and work this part of the
problem. Click the pens to continue
Third, combine the other side.
Pick my nose to continue
Algebra
Geek
Patrol
Write this problem in the box on your worksheet.
60
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
Congratulations Only one problem left until another Geek
Pen.Aren’t you excited?
61
2
One Step Equations
X - 6 = 14
This time you are going to work the problem on your paper first and then we will go through it.
Pick my nose when you are finished
Are you sure you are done? Check your answer before
moving on.
Algebra
Geek
Patrol
Go ahead and give it a try!
I won’t tell anyone.
Write this problem in the box on your worksheet.
62
Make sure you have copied all the steps on your paper and then click on Buck.
2
One Step Equations
X - 6 = 14_________ + 6 +6
X = 20 First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.
Click the pens to continue
Algebra
Geek
Patrol
63
Now, try these on your own! X – (-2) = 7 X – 5 = -8 X – (-3) = 0
64
Algebra Geek Patrol
One Step Equations
Jeepers!You get another Geek
Pen.Come back soon to try more!
Pick my nose to continue
Algebra
Geek
Patrol
65
Thursday 10/20/11
2-5 Solving Equations Containing Integers
pg. 100
Essential Question
How can you solve equations that contain integers?
68
Algebra Geek Patrol
The Pocket Protectors of Algebra
69
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
What’s the same as yesterday?
The word we know and love…
Opposite!
Welcome Back!
70
Now another set. Make sure to write your answers on your paper, and when you are finished click on me.
Pick my nose to continue
Add = __________
Subtract = __________
Multiply = __________
Divide = __________
71
Your answers should have been…
Pick my nose to continue
Add = __________
Subtract = __________
Multiply = __________
Divide = __________
Subtract
Add
Divide
Multiply
72
One last set. Make sure to write your answers on your paper, and when you are finished click on me.
Pick my nose to continue
+ = __________
- = __________
x = __________
÷ = __________
73
Your answers should have been…
Pick my nose to continue
+ = __________
- = __________
x = __________
÷ = __________
-
+
÷
x
74
Who REMEMBERS?
What are the 3 steps to solve a one step equation? I___________ S___________ C___________
74
Steps to Solving Equations:
1. ISOLATE the variable by doing the opposite, Inverse, Operation.
2. SOLVE the equation.3. CHECK your solution.
76
1
One Step Equations
Click on the answer below that is the opposite of x 2.
+ 2- 2
x 2
÷ 2
2x = 18
Algebra
Geek
Patrol
Write this problem in the box on your worksheet.
77
1
One Step Equations
Not quite.
Remember, we are looking for the opposite of x 2.
Click on Buck and give it another try.
Algebra
Geek
Patrol
78
You remember from working with fractions, what happens when one number is divided by the same number?
÷ ÷ ___ __2x 181
One Step Equations
Yes!
So, let’s put ÷ 2 on each side of the equation.
2x = 18 2 2_________
Another way to write ÷ 2 is with a fraction bar. Like this.
This makes the left side a fraction.
Click on the pens when you are ready.
X = Look at the right side. All we have left is 18 divided by 2. So, what is 18 ÷ 2?
9 That just leaves X on the left side.Copy the entire problem and solution above on your paper, and then click on Buck.
=
Algebra
Geek
Patrol
That’s right! It cancels
out. That’s right! X = 9
79
3 33x = 152
One Step Equations
Rama-Lama–Ding-Dong
Make sure you have copied all the steps on your paper and then click on Buck.
This time I am going to give you the steps, which you will need to write down, and then you will do
the problem on your paper.
First, put the opposite on both sides.Remember to rewrite it as a fraction.
Write this on your paper, and work this part of the
problem.Click the pens to continue
Third, combine the other side.
Pick my nose to continue
Don’t worry. It’s a Geek Thing.
÷ ÷ ___ __3x 15
X =
=
Algebra
Geek
Patrol
Second, cancel out one side.
5
Write this problem in the box on your worksheet.
80
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
Congratulations, Now let’s try one last problem.
81
3
One Step Equations
Algebra
Geek
Patrol
This time you are going to work the problem on your paper first and then we will go through it.
Pick my nose when you are finished
Are you sure you are done? Check your answer before
moving on.
Go ahead and give it a try!I’ve been sworn to secrecy.
4x = 24Write this problem in the box on your worksheet.
82
___ __4x 244x = 243
One Step Equations
First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.Make sure you have copied all the steps on your paper and then click on Buck.
Click the pens to continue
4 4X =
=
6
Algebra
Geek
Patrol
83
3
One Step Equations
Great!Your future’s so bright,
I gotta wear shades.
Actually,
I already am.
Pick my nose to continue
Algebra
Geek
Patrol
84
Now, try these on your own! -5x = -100 12x = -144 X – (-3) = 0
85
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
Now for the final part. Just remember Opposite, and you are done.
As Always, Geek Luck!
86
1
One Step Equations
Click on the answer below that is the opposite of ÷3.
+ 3- 3
x 3
÷ 3
x 3
= 12
Algebra
Geek
Patrol
87
1
One Step Equations
Doh! Not Really.
Remember, we are looking for the opposite of ÷ 3.
Click on Buck and give it another try.
Algebra
Geek
Patrol
88
You remember from working with fractions, what happens when one number is divided by the same number?
1
One Step Equations
That’s It!
So, let’s put●3 on each side of the equation. Remember,●means times.
Now, the left side cancels out just like a fraction.
Click on the pens when you are ready.
X = Look at the right side. All we have left is 12 times 3. So, what is 12 times 3?
36
Copy the entire problem and solution above on your paper, and then click on Buck.It cancels out.
x 3
= 12
Algebra
Geek
Patrol
3• •3
That’s Right!
Write this problem in the box on your worksheet.
89
2
One Step Equations
Make sure you have copied all the steps on your paper and then click on Buck.
This time I am going to give you the steps, which you will need to write down, and then you will do
the problem on your paper.
First, put the opposite on both sides.
Write this on your paper, and work this part of the
problem.Click the pens to continue
Third, combine the other side.
Pick my nose to continue
Second, cancel out one side.
x 7
= 3
Algebra
Geek
Patrol
7 x x 7
X = 21
Write this problem in the box on your worksheet.
90
One Step Equations
Algebra Geek Patrol
Pick my nose to continue
And Now…. (Drum Roll, Please)
THE LAST Practice PROBLEM!
91
3
One Step Equations
Algebra
Geek
Patrol
This time you are going to work the problem on your paper first and then we will go through it.
Pick my nose when you are finished
Are you sure you are done? Check your answer before moving
on.
Go ahead and give it a try!
I can’t tell anyone. I don’t even have a mouth.
x 5
= 6Write this problem in the box on your worksheet.
92
5 x3
One Step Equations
First, put the opposite on both sides.Second, cancel out one side.Third, combine the other side.
Make sure you have copied all the steps on your paper and then click on Buck.
Click the pens to continue
x 5
= 6 x 5
X = 30
Algebra
Geek
Patrol
93
Now, try these on your own! X / -10 = 5 X / -9 = -8
94
Algebra Geek Patrol
One Step Equations
You’re a GEEK!I’m so happy,
I could cry
Pick my nose to continue
Congratulations!
Algebra
Geek
Patrol
95
What? You want more?You really are a geek.
More Practice AHEAD!
Solve each question. Check each answer.
Example 1
–6 + x = –7
–6 + x = –7+ 6 + 6
x = –1
Check
–6 + x = –7
–6 + (–1) = –7
–7 = –7
Professor Burger the Math Man Example
http://my.hrw.com/math06_07/nsmedia/homework_help/msm2/msm2_ch02_05_homeworkhelp.html
Example 2Solve each equation. Check each answer.
y – 9 = –40
y – 9 = –40+ 9 + 9
y = –31
Check
–31 – 9 = –40?
y – 9 = –40
–40 = –40?
Example 3Solve each equation. Check each answer.
c4
= –24
c4
= –24
c4 = 4(–24)4
c = –96
Check
c4
= –24
–964
= –24
–24 = –24
Professor Burger the Math Man Example
http://my.hrw.com/math06_07/nsmedia/homework_help/msm2/msm2_ch02_05_homeworkhelp.html
Example 4Solve each equation. Check each answer.
–400 = 8y
–400 = 8y
–400 = 8y
8 8
–50 = y
Check
–400 = 8y
–400 = 8(–50)
–400 = –400
Professor Burger the Math Man Example
http://my.hrw.com/math06_07/nsmedia/homework_help/msm2/msm2_ch02_05_homeworkhelp.html
In 2003, a manufacturer made a profit of $300 million. This amount was $100 million more than the profit in 2002. What was the profit in 2002?
Example 5
Let p represent the profit in 2002 (in millions of dollars).
This year’s profit300
is =
300 = 100 + p–100 –100
200 = p
The profit was $200 million in 2002.
100 million100
More than +
Last year’s profitp
Match the Equation with its Answer…
Take out a separate sheet of paper. Write your name date and period at
the top. Write each equation. Show your work. Match the question card (blue) with
the answer card (yellow).
Addition
X + 5 = -9 X + 5 - 5 = -9 -5 X = -14
-6 + X = -4 -6 + 6 + X = -4 + 6 X = 2
Try the following on your paper.
10 = X + 3
5 + X = 9
6 = 3 + X
Answers!!!
X = 7
X = 4
X = 3
Equations with subtraction
X - 5 = 8 X - 5 + 5 = 8+5 X = 13
5 - X = 6 5 - 5 + X = 6 - 5 X = 1
Try the following on your paper.
X - 7 = -1
X - 4 = 66
8 = X - 2
-8 = X - 2
Answers!!!
X = 6
X = 70
X = 10
X = -6
Multiplication of Equations
3X = -9 3X/3 = -9/3 X = -3
-5X = -40 -5X/-5 = -40/-5 X = 8
Try these on your paper.
4X = -16
-1X = 9
6 = 5X
12X = 3
Answers!!!
X = -4
X = -9
X = 6/5
X = 1/4
Division of Equations
1/2X = 4 (2/1)1/2X = 4(2) X = 8
-3/4X = 6 (-4/3)(-3/4)X = 6(-4/3) X = -8
Try these on your paper.
X/3 = 9
-X/4 = 7
1/3X = -1
4 = X/4
Answers!!!
X = 27
X = -28
X = -3
X = 16
Write the following on your paper for a quiz grade.1) _4X = 15
2) X/2 = -8
3) 9 - X = -1
4) -12 + X = 0
5) -X/3 = 4
6) X + 5 = 5
7) X - 4 = 4
7) -X = 5
8) X + 50 =-50
8) X/5 = -55